Effective coherence of groups discriminated by a locally quasi-convex hyperbolic group

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Publication

We prove that every finitely generated group G discriminated by a locally quasiconvex torsion-free hyperbolic group is effectively coherent: that is, presentations for finitely generated subgroups can be computed from the subgroup generators. We study G via its embedding into an iterated centralizer extension of , and prove that this embedding can be computed. We also give algorithms to enumerate all finitely generated groups discriminated by and to decide whether a given group, with decidable word problem, is discriminated by . If may have torsion, we prove that groups obtained from by iterated amalgamated products with virtually abelian groups, over elementary subgroups, are effectively coherent.